Quantifying the spatiotemporal evolution of the turbulent horseshoe vortex in front of a vertical cylinder

Abstract

The spatiotemporal evolution of the turbulent horseshoe vortex (THV) in front of a cylinder vertically mounted on a hydraulically smooth flat-bed was physically modeled in a large water flume. A particle image velocimetry (PIV) system with upward-illumination was, in particular, employed for the junction flow visualization. The examined Reynolds number was varied from 1.28 × 104 to 1.08 × 105, which is above the threshold of turbulent transition for a junction flow. Based on the PIV measurements, the characteristic features were presented for both the time-averaged and the instantaneous flow fields in a sheet flow at the upstream wall-cylinder junction. Statistical analyses on the experimental data are performed to characterize the spatial-temporal evolution of THV strength. The normalized THV strength in the time-averaged flow field increases first and then approaches a constant value with increasing the ratio of cylinder diameter to water depth. Two alternating patterns, i.e., the regular oscillation and the random wandering, are identified for the quasi-periodic oscillating behaviors of the instantaneous THV. It is found that the cumulative distribution curves for the normalized instantaneous THV strength can be described by the Weibul distribution. The present results provide a physical insight and quantitative characterization for the spatiotemporal evolution of THV, which is critical for predicting the associated wall shear stresses.